Swammerdami
Squadron Leader
(No posts in this subforum for three months.)
Here's a nifty puzzle in arithmetic I just stumbled upon. It's too easy to excite serious mathematicians, but hard enough to challenge talented amateurs. Perfect!
Consider numbers that are equal to the sum of two or more consecutive positive integers. For examples 3=1+2; 9=2+3+4; 26=5+6+7+8.
Two puzzles:
(1) Determine the set of positive integers which CAN be expressed as the sum of two or more consecutive positive integers.
(Or equivalently, Determine the set of positive integers which CANNOT be expressed as the sum of two or more consecutive positive integers.)
(2) Prove your result.
(Nitpicking detail: replace "positive" with "non-negative" and one more case emerges: 1=0+1. Treat this special case whichever way you prefer.)
Here's a nifty puzzle in arithmetic I just stumbled upon. It's too easy to excite serious mathematicians, but hard enough to challenge talented amateurs. Perfect!
Consider numbers that are equal to the sum of two or more consecutive positive integers. For examples 3=1+2; 9=2+3+4; 26=5+6+7+8.
Two puzzles:
(1) Determine the set of positive integers which CAN be expressed as the sum of two or more consecutive positive integers.
(Or equivalently, Determine the set of positive integers which CANNOT be expressed as the sum of two or more consecutive positive integers.)
(2) Prove your result.
(Nitpicking detail: replace "positive" with "non-negative" and one more case emerges: 1=0+1. Treat this special case whichever way you prefer.)